What is the possessive in this sentence all of children got a memory book?

The possessive in the sentence "All of the children got a memory book" is "the children's".

Here's why:

* "Children" is the noun we want to show possession of.

* "The" is the definite article modifying the noun.

* We add "'s" to the end of the plural noun "children" to indicate that the memory book belongs to all of the children.

Therefore, the complete possessive phrase is "the children's".